The stability of relativistic stars and the role of the adiabatic index

Moustakidis, Ch. C.

doi:10.1007/s10714-017-2232-9

Cited by 184 publications

(63 citation statements)

References 43 publications

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“…In this representation we find the Newtonian limit γ c = 4/3 as p c → 0, and we can see that γ c grows linearly with the central pressure of the star. These results are once again in good agreement with those in [37].…”

Section: Radial Stability Above the Buchdahl Boundsupporting

confidence: 91%

On the radial stability of ultra-compact Schwarzschild stars beyond the Buchdahl limit

Posada

Chirenti

2019

Class. Quantum Grav.

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In this paper we used the theory of adiabatic radial oscillations developed by Chandrasekhar to study the conditions for dynamical stability of constant energydensity stars, or Schwarzschild stars, in the unstudied ultra compact regime beyond the Buchdahl limit, that is, for configurations with radius R in the range R S < R < (9/8)R S , where R S is the Schwarzschild radius of the star. These recently found analytical solutions exhibit a negative pressure region in their centre and, in the limit when R → R S , the full interior region of the star becomes filled with negative pressure. Here we present a systematic analysis of the stability of these configurations against radial perturbations. We found that, contrary to the usual expectation found in many classical works, the ultra compact Schwarzschild star is stable against radial oscillations. We computed values of the critical adiabatic index γ c for several stellar models with varying radius R/R S and found that it also approaches a finite value as R/R S → 1.

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Section: Radial Stability Above the Buchdahl Boundsupporting

confidence: 91%

On the radial stability of ultra-compact Schwarzschild stars beyond the Buchdahl limit

Posada

Chirenti

2019

Class. Quantum Grav.

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“…Figure 3 (below) shows that the adiabatic index r (r ) > 4/3 for our solutions with positive anisotropy. More strict condition on adiabatic index for stable region was derived by Moustakidis [61] and found that the critical value of adiabatic index crit depends on ξ -parameter (amplitude of lagrangian displacement from equilibrium) and compactness parameter β = M/R. On assuming particular form of ξ -parameter he obtained the constraint as…”

Section: Adiabatic Indexmentioning

confidence: 99%

Compact star models in class I spacetime

et al. 2019

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In the present article, we have presented completely new exact, finite and regular class I solutions of Einstein's field equations i.e. the solutions satisfy the K armarkar condition. For this purpose needfully we have introduced a completely new suitable g rr metric potential to generate the model. We have investigated the various physical aspects for our model such as energy density, pressure, anisotropy, energy conditions, equilibrium, stability, mass, surface and gravitational red-shifts, compactness parameter and their graphical representations. All these physical aspects have ensured that our proposed solutions are wellbehaved and hence represent physically acceptable models for anisotropic fluid spheres. The models have satisfied causality and energy conditions. The presented models are also stable by satisfying Bondi condition and Abreu et al. condition, in equilibrium position and static by satisfying TOV equation, Harrison-Zeldovich-Novikov condition, respectively. For the parameters chosen in the paper are matching in modeling Vela X-1, Cen X-3, EXO 1785-248 and LMC X-4. The M-R graph generated from the solutions is matching the ranges of masses and radii for the considered compact stars. This work also estimated the approximate moment of inertia for the mentioned compact stars.

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“…For the anisotropic fluid sphere, if the stability depends on the type of anisotropy then the situation becomes more complicated [100,101]. A recent work by Moustakidis [103] reveals that the critical value of adiabatic index strongly depends on the M/R. The critical value was found to be Figure 15, confirms that the model under consideration is stable, due to the adiabatic index is greater than 4/3.…”

Section: Adiabatic Index and Stability Conditionmentioning

confidence: 62%

Minimally deformed anisotropic model of class one space-time by gravitational decoupling

et al. 2019

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In this article, we have presented a static anisotropic solution of stellar compact objects for selfgravitating system by using minimal geometric deformation techniques in the framework of embedding class one spacetime. For solving of this coupling system, we deform this system into two separate system through the geometric deformation of radial components for the source function λ(r) by mapping: e −λ(r) → e −λ(r) + β g(r), where g(r) is deformation function. The first system corresponds to Einstein's system which is solved by taking a particular generalized form for source functionλ(r) while another system is solved by choosing well-behaved deformation function g(r). To test the physical viability of this solution, we find complete thermodynamical observable as pressure, density, velocity, and equilibrium condition via. TOV equation etc. In addition to the above, we have also obtained the moment of inertia (I), Kepler frequency (v), compression modulus (K e) and stability for this coupling system. The M-R curve has been presented for obtaining the maximum mass and corresponding radius of the compact objects.

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The stability of relativistic stars and the role of the adiabatic index

Cited by 184 publications

References 43 publications

On the radial stability of ultra-compact Schwarzschild stars beyond the Buchdahl limit

On the radial stability of ultra-compact Schwarzschild stars beyond the Buchdahl limit

Compact star models in class I spacetime

Minimally deformed anisotropic model of class one space-time by gravitational decoupling

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